Optimal single-shot strategies for discrimination of quantum measurements

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Authors

SEDLÁK Michal ZIMAN Mário

Year of publication 2014
Type Article in Periodical
Magazine / Source Physical Review A
MU Faculty or unit

Faculty of Informatics

Citation
Web http://dx.doi.org/10.1103/PhysRevA.90.052312
Doi http://dx.doi.org/10.1103/PhysRevA.90.052312
Field Information theory
Keywords quantum measurement; hypothesis testing; quantum key distribution
Description We study discrimination of m quantum measurements in the scenario when the unknown measurement with n outcomes can be used only once. We show that ancilla-assisted discrimination procedures provide a nontrivial advantage over simple (ancilla-free) schemes for perfect distinguishability and we prove that inevitably m <= n. We derive necessary and sufficient conditions of perfect distinguishability of general binary measurements. We show that the optimization of the discrimination of projective qubit measurements and their mixtures with white noise is equivalent to the discrimination of specific quantum states. In particular, the optimal protocol for discrimination of projective qubit measurements with fixed failure rate (exploiting maximally entangled test state) is described. While minimum error discrimination of two projective qubit measurements can be realized without any need of entanglement, we show that discrimination of three projective qubit measurements requires a bipartite probe state. Moreover, when the measurements are not projective, the non-maximally entangled test states can outperform the maximally entangled ones.
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